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Given a point set P={x_n}_(n=0)^(N-1) in the s-dimensional unit cube [0,1)^s, the star discrepancy is defined as D_N^*(P)=sup_(J in Upsilon^*)D(J,P), (1) where the local ...

Given a point set P={x_n}_(n=0)^(N-1) in the s-dimensional unit cube I=[0,1)^s, the star discrepancy is defined as D_N^*(P)=sup_(J in Upsilon^*)D(J,P), (1) where the local ...

The geometric distribution is a discrete distribution for n=0, 1, 2, ... having probability density function P(n) = p(1-p)^n (1) = pq^n, (2) where 0<p<1, q=1-p, and ...

The number q in a fraction p/q.

Connecting the centers of touching spheres in a three-dimensional Apollonian gasket by edges given a graph known as the Apollonian network. This process is illustrated above ...

The number 13.

A friend of a number n is another number m such that (m,n) is a friendly pair.

The happy end problem, also called the "happy ending problem," is the problem of determining for n>=3 the smallest number of points g(n) in general position in the plane ...

The average number of regions into which n randomly chosen planes divide a cube is N^_(n)=1/(324)(2n+23)n(n-1)pi+n+1 (Finch 2003, p. 482). The maximum number of regions is ...

A Poisson process is a process satisfying the following properties: 1. The numbers of changes in nonoverlapping intervals are independent for all intervals. 2. The ...